On the rationality problem for hypersurfaces

Jan Lange; Stefan Schreieder

doi:10.48550/arXiv.2409.12834

On the rationality problem for hypersurfaces

Jan Lange, Stefan Schreieder

Institut für Algebraische Geometrie

Publikation: Arbeitspapier/Preprint › Preprint

Abstract

We show that a very general hypersurface of degree d at least 4 and dimension at most $(d+1)2^{d-4}$ over a field of characteristic different from 2 does not admit a decomposition of the diagonal; hence, it is neither stably nor retract rational, nor $\mathbb{A}^1$-connected. Similar results hold in characteristic 2 under a slightly weaker degree bound. This improves earlier results by the second named author and Moe.

Originalsprache	Englisch
DOIs	https://doi.org/10.48550/arXiv.2409.12834
Publikationsstatus	Elektronisch veröffentlicht (E-Pub) - 19 Sept. 2024

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10.48550/arXiv.2409.12834Lizenz: Arxiv nonexclusive-distrib 1.0

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